Room temperature chirality switching and detection in a helimagnetic MnAu2 thin film

Helimagnetic structures, in which the magnetic moments are spirally ordered, host an internal degree of freedom called chirality corresponding to the handedness of the helix. The chirality seems quite robust against disturbances and is therefore promising for next-generation magnetic memory. While the chirality control was recently achieved by the magnetic field sweep with the application of an electric current at low temperature in a conducting helimagnet, problems such as low working temperature and cumbersome control and detection methods have to be solved in practical applications. Here we show chirality switching by electric current pulses at room temperature in a thin-film MnAu2 helimagnetic conductor. Moreover, we have succeeded in detecting the chirality at zero magnetic fields by means of simple transverse resistance measurement utilizing the spin Berry phase in a bilayer device composed of MnAu2 and a spin Hall material Pt. These results may pave the way to helimagnet-based spintronics.

Helimagnetic structures, in which the magnetic moments are spirally ordered, host an internal degree of freedom called chirality corresponding to the handedness of the helix.The chirality seems quite robust against disturbances and is therefore promising for next-generation magnetic memory.While the chirality control was recently achieved by the magnetic field sweep with the application of an electric current at low temperature in a conducting helimagnet, problems such as low working temperature and cumbersome control and detection methods have to be solved in practical applications.Here we show chirality switching by electric current pulses at room temperature in a thin-film MnAu 2 helimagnetic conductor.Moreover, we have succeeded in detecting the chirality at zero magnetic fields by means of simple transverse resistance measurement utilizing the spin Berry phase in a bilayer device composed of MnAu 2 and a spin Hall material Pt.These results may pave the way to helimagnet-based spintronics.
In solids, an internal degree of freedom emerges upon a phase transition involving symmetry breaking.For example, a ferroelectric phase transition breaks the space inversion symmetry and induces spontaneous electric polarization.The two states with positive and negative polarizations are completely degenerate in the absence of electric fields, and therefore the polarization can be viewed as an internal degree of freedom.The application of electric fields can switch the sign of electric polarization.Such a controllable internal degree of freedom is useful for memorizing information and is therefore applicable to memory storage devices.Indeed, random-access memories based on ferroelectrics have been fabricated and are commercially available 1,2 .
A more important example is a ferromagnet.In the ferromagnetic state, the time-reversal symmetry is broken, and the magnetization is the internal degree of freedom, which can be controlled by a magnetic field.Hard disk drives utilize ferromagnets, and magnetic randomaccess memory (MRAM) has also been developed 3,4 .One of the major obstacles for high-density MRAM is stray fields.As the bit scale is decreased, the magnetizations of separated ferromagnets do not work as independent degrees of freedom owing to the entanglement caused by stray fields.
In order to resolve this issue, spintronics based on antiferromagnets is currently attracting considerable attention [5][6][7][8] .A helical magnet 9 is one form of antiferromagnet that has unique characteristics: Mirror symmetry is broken, and the chirality works as an internal degree of freedom unless the crystal structure is noncentrosymmetric.The chirality does not couple to the magnetic field and is invariant under any translation and rotation.In order to reverse it, one has to first straighten the spin direction and wind it reversely.In other words, the helimagnetic memory is topologically protected in that way and should be stable even in a very small device.Therefore, this seems to be a desirable degree of freedom for next-generation magnetic storage.Nevertheless, the chirality in conducting helimagnets that are compatible with spintronic devices had been uncontrollable until recently, whereas the chirality in insulating helimagnets is known to be controllable with an electric field 10,11 .
Recently Jiang et al. 12 showed that the degeneracy relevant to the chirality is lifted by the simultaneous application of magnetic fields and electric currents with a mechanism totally different from the insulating case.Figure 1a illustrates a conduction electron and localized moments in a helimagnet.The spin of the conduction electrons is aligned to the localized moments owing to the s-d exchange coupling J sd .When a conduction electron propagates along the propagation vector of the helimagnet, the spin rotates around the propagation vector, giving rise to the spin transfer torque on localized magnetic moments.The adiabatic spin transfer torque rotates the magnetic structure around the propagation vector and non-adiabatic and damping torques deform it conically [13][14][15] .The net magnetization direction of the conical magnetic structure depends on the chirality.By additionally applying a magnetic field parallel to the conical magnetization, the chiral degeneracy is lifted.In other words, the favored chirality depends on whether the electric current is parallel or antiparallel to the magnetic field as illustrated in Fig. 1b.Based on this mechanism, Jiang et al. demonstrated chirality control at temperatures around 50 K in a microfabricated single crystal piece of MnP helimagnetic conductor.However, the method used to control the chirality involved a complex sequence of current and magnetic field changes.For practical devices, a more straightforward approach for switching the chirality is needed.It must operate at room temperature, and in thin films to be suitable for industrial fabrication, with easy readout of the chirality.
In this work, we show room-temperature chirality control in a thinfilm MnAu 2 helimagnet by solely applying an electric current pulse in a magnetic field.Moreover, we show the chirality can be probed by the transverse resistance at zero magnetic fields in a bilayer device composed of MnAu 2 and a spin Hall material Pt, which originates from the spin Berry phase (Fig. 1c).

Properties of MnAu 2 thin film sample
MnAu 2 crystallizes into a centrosymmetric tetragonal crystal structure with the space group I4/mmm 16 .The Mn magnetic moments show a helical magnetic order with a helical plane perpendicular to the propagation vector q = (0, 0, 0.28) in the reciprocal lattice unit, corresponding to the helical pitch of 3.1 nm 17 .The transition temperature is reported to be as high as T c = 360 K 18 .We prepared single-crystal films of MnAu 2 with a thickness of 100 nm on hexagonal ScMgAlO 4 (10-10) substrates.X-ray diffraction (XRD) measurements revealed that the MnAu 2 thin films are stacked along the [110] direction so that the helical propagation vectors are parallel to the thin films (Fig. 2a, b, see "Methods" section and Supplementary Fig. 3 for more detail).The magnetic susceptibility M/H along the [001] direction shows a clear kink at 335 K (Fig. 2c).The resistivity ρ shows metallic temperature dependence with a cusp-like anomaly also around 335 K, as shown in Fig. 2d.The anomalies can be ascribed to the helical transition temperature [18][19][20] , which is slightly lower than the reported value presumably because of epitaxial strain.Similar kinks appear in the magnetic field dependences of magnetization and resistivity.Figure 3a shows the magnetization and magnetoresistance curves for H || [001] at 300 K, in which clear kinks are observed at 1.5 T. Above the kink field, the magnetization is saturated, which indicates that they are caused by the transition from the helical phase to the induced-ferromagnetic (FM) phase 18,20 .The transition field increases as the temperature is lowered, as shown in Fig. 2e.

Chirality control by magnetic field sweep
We first demonstrate chirality control at room temperature by means of a magnetic field sweep with the application of an electric current, similar to Jiang et al. 12 A magnetic field H 0 = ±3 T and a dc electric current j 0 were first applied along the helical propagation vector.The magnetic field and the electric current were parallel (H 0 > 0, j 0 > 0 or H 0 < 0, j 0 < 0) or antiparallel (H 0 > 0, j 0 < 0 or H 0 < 0, j 0 > 0).Then, we swept the magnetic field to 0 T and turned off the dc electric current.
After this control procedure, we read out the controlled chirality utilizing the nonreciprocal electronic transport (NET) [21][22][23][24][25][26][27] , which is a fieldasymmetric component of the second-harmonic resistivity ρ 2ω measured by an ac electric current, ρ 2ω asym (H) = [ρ 2ω (+H) − ρ 2ω (−H)]/2.Note that ρ 2ω has the same unit as the ordinary resistivity and is proportional to the applied current (see Supplementary Fig. 5).The NET shows up only when the inversion and time-reversal symmetries are simultaneously broken.It reverses its sign upon a space-inversion or time- reversal operation (see Supplementary Information, section 2).Since the chirality is reversed upon the space-inversion operation, the sign of NET probes the chirality 12,21,[24][25][26][27] .In order to obtain ρ 2ω asym (H), we measured ρ 2ω (H) while increasing H from 0 to 3 T and that also while decreasing H from 0 to −3 T and calculated the difference.Figure 3b shows the magnetic field dependence of the NET signal ρ 2ω asym (H) after the field sweep chirality control with H 0 = ±3 T and j 0 = 0, ±8.0 × 10 9 A/ m 2 .While ρ 2ω asym (H) was almost negligible for j 0 = 0, finite ρ 2ω asym (H) was observed for the other data.The magnitude steeply increases as the field magnitude is increased from 0 T. It shows a maximum around 0.5 T and almost vanishes above the ferromagnetic transition field.We confirm the magnetic field angle dependence of ρ 2ω asym (H) is consistent with the chiral symmetry (see Supplementary Figs. 5, 6 for more detail).Importantly, the sign of the NET signal depends on whether H 0 and j 0 are parallel or antiparallel, confirming that the chirality was controlled successfully.The inset for Fig. 3b shows the j 0 dependence of the NET signal.The NET signal monotonically increases with j 0 and saturates around j 0 = 6.0 × 10 9 A/m 2 , suggesting that the controlled volume fraction approaches unity.

Chirality switching by electric current pulses
Then, we performed the chirality control by the application of electrical current pulses.A theory in the literature 28 showed that the chirality can be controlled by the application of an electrical current pulse under a small magnetic field in the helimagnetic state when the magnitude of the electric current is much larger.The simple switching largely increases the availability of the chiral degree of freedom in spintronic devices.To experimentally demonstrate the chirality switching, we first swept the magnetic field from the high field to zero without an electric current so that the two chiral domains are almost equally distributed (see Fig. 3b), and then applied positive and negative electrical pulses with a duration of 1 ms alternately every 15 min at 0.5 T while measuring the second-harmonic resistivity.Figure 4a shows the time dependence of the second-harmonic resistivity change  asym (H) at 300 K after the chirality control by the magnetic field sweep from the magnetic field H 0 (H 0 = ± 3 T) with the application of electric current j 0 = 0, ±8.0 × 10 9 A/m 2 .ρ 2ω asym (H) is the anti-symmetric part of the second-harmonic electrical resistivity ρ 2ω (H), viz., ρ 2ω asym (H) = [ρ 2ω (+H) − ρ 2ω (−H)]/2.ρ 2ω (+H) and ρ 2ω (−H) were independently measured just after the chirality control.The ac electric current used for the ρ 2ω (H) measurement is 2.0 × 10 9 A/m 2 .The inset shows the j 0 dependence of |ρ 2ω asym (H)| at 0.5 T.
Δρ 2ω after the zero current field sweep.When the pulse current j p was larger than 15 × 10 9 A/m 2 , a discontinuous change of Δρ 2ω appeared.The magnitude of the discontinuous change increases as the current is increased, and the negative pulse reversed Δρ 2ω .We observed the alternating change of Δρ 2ω several times.Note that the magnitude of Δρ 2ω is not increased by the multiple pulse application, and that the linear resistivity does not show the discontinuous change (see Supplementary Fig. 7).To confirm that such a discontinuous change of the second-harmonic resistivity corresponds to the chiral domain change, we measured the field dependence of the second-harmonic resistivity after the application of an electric current pulse at 0.5 T. For this experiment, we also performed a zero-current magnetic field sweep from 3 to 0 T before the pulse application.After the pulse application, we decreased the magnetic field to −0.5 T and restored it to +0.5 T while measuring the second-harmonic resistivity.The measured second-harmonic resistivity data are shown in Fig. 4b.In this figure, the difference from the zero-field value is plotted just for clarity.The asymmetric field dependence is clearly observed, and its sign depends on that of the current pulse.These results show that the discontinuous change of the second-harmonic resistivity is certainly caused by the chiral domain change.
We discuss the j p dependence of ρ 2ω asym estimated from the magnetic field dependence after the pulse application (Fig. 4c).ρ 2ω asym sharply increases around 1.4 × 10 10 A/m 2 and saturates around 1.9 × 10 10 A/m 2 .For comparison, we reproduce the electric current dependence of ρ 2ω asym for the field sweep control case.A much larger electric current is needed for the switching but the magnitude of the controlled ρ 2ω asym is comparable with the sweeping case, suggesting that the controlled volume fraction approaches unity also for the pulse case.Thus, chiral domain switching is achieved for this thin film sample.Nevertheless, it should be noted that the heating effect seemed to assist the switching phenomenon.The sample resistance estimated from the voltage during the pulse application is larger than that at 300 K, indicating heating of the sample (see Supplementary Fig. 8).The estimated sample temperature T sam is plotted against j p .The threshold current density j p = 1.4 × 10 10 A/m 2 corresponds to the sample temperature of 318 K, which is lower than the transition temperature 335 K.It gradually increases and exceeds the transition temperature 335 K around 2 × 10 10 A/m 2 .In this case, the chirality was erased by the increase of temperature but perhaps controlled again at a moment when the magnitude of the electric current was decreased.When the nominal experimental temperature is decreased to 290 K the j p dependence is also shifted, which suggests that the heating effect certainly contributes to the chiral switching phenomenon (see Supplementary Fig. 9).The critical current of chirality domain control is expected to decrease with increasing temperature toward T c = 335 K. Presumably, it becomes low enough around 318 K for the chirality switching, and finite ρ 2ω asym is observed above 1.4 × 10 10 A/m 2 .Traversing the helical transition temperature is not mandatory in this phenomenon.

Chirality-dependent transverse resistance in a MnAu 2 /Pt bilayer device
Finally, we show that the chirality can be probed by a simple transverse resistance measurement in a MnAu 2 /Pt bilayer device (Fig. 1c).The origin of the transverse resistance can be explained by the following two steps.First, an electric current along the helimagnetic wave vector induces spin accumulation depending on the chirality in the helimagnetic MnAu 2 layer.Next, the accumulated spin is diffused to the Pt layer and induces a transverse voltage by means of the inverse spin Hall effect (ISHE) [29][30][31] .While the mechanism of the second step is well known 32,33 , we explain the first step microscopically below.As shown in Fig. 1a, when a conduction electron propagates along the propagation vector of the helimagnet, the spin rotates around the propagation vector with a sense that depends on the chirality.The chiralitydependent spin rotation affects the dynamics of the conduction electron through the fictitious vector potential (Berry connection) A = iγqσ x ,0,0 À Á , where the x-axis is along the propagation vector of the helimagnet, q is the magnitude of the propagation vector, γ = ±1 is the chirality handedness, and σx is the Pauli matrix 34,35 .Therefore, when an electric current j = ( j x , 0, 0) is applied, the current-dependent energy gives rise to spin polarization depending on the chirality.This phenomenology was numerically investigated for a helimagnet induced by the Dzyaloshinskii-Moriya interaction with the fixed chirality in the literature 34 .We confirmed the validity also for a variable-chirality helimagnetic model (see Supplementary Information, Section 1).
To experimentally demonstrate the transverse resistance originating from the chirality-dependent spin accumulation, we prepared bilayer devices consisting of MnAu 2 and Pt on hexagonal ScMgAlO 4 Fig. 4 | Chirality switching.a Temporal variation of second-harmonic resistivity change Δρ 2ω at 300 K and 0.5 T with the alternate application of positive and negative electric current pulses with a duration of 1 ms.Before the measurement, the magnetic field is swept from 3 to 0 T without electric current so that two different chirality domains are equally distributed.The magnitudes of the pulse currents are |j p | = 15 (blue), 16 (green), 17 (magenta), and 18 (red) × 10 9 A/m 2 .b Magnetic field dependence of ρ 2ω at 300 K after application of the current pulses at 0.5 T. The pulse currents are j p = 0 (black), +16 × 10 9 A/m 2 (green, filled), −16 × 10 9 A/m 2 (green, open), +18 × 10 9 A/m 2 (red, filled), −18 × 10 9 A/m 2 (red, open), +20 × 10 9 A/m 2 (orange, filled) and −20 × 10 9 A/m 2 (orange, open).Before the measurement, the magnetic field is swept from 3 to 0 T without an electric current, similarly to the case of Fig. 4a.c ρ 2ω asym at 300 K and 0.5 T as a function of j p (redfilled circles).The j 0 dependence of ρ 2ω asym in the case of field sweep control is reproduced from Fig. 3b for comparison (blue-filled circles).The red-open circles indicate the sample temperature T sam during the applied current pulse j p estimated from the sample resistance (see Supplementary Fig. 8 for more detail).substrates (see "Methods" and Supplementary Figs. 4, 10).Similarly to the MnAu 2 sample without Pt shown above, the helical propagation vector along the [001] direction is parallel to the film plane.The Pt layer with a thickness of 10 nm was deposited on MnAu 2 .When an electric current I is applied along the MnAu 2 [001] direction, the chirality-dependent accumulated spin moment should diffuse to the Pt layer, and a transverse voltage V T is expected to emerge owing to the ISHE as schematically shown in Fig. 1c.Therefore, the chirality should be probed by the transverse resistance R T = V T /I.
Figure 5 demonstrates the observation of chirality-dependent transverse resistance at 260 K in the MnAu 2 /Pt bilayer device.We first reproduced the field sweep chirality control and the NET signal for the bilayer device for comparison with the transverse resistance.asym at 260 K measured after the magnetic field sweep from H 0 = ±5 to 0 T with the application of a dc electric current I 0 = ±8 mA (H 0 > 0 for Fig. 5a and H 0 < 0 for Fig. 5b).Finite NET signals were clearly observed in the helimagnetic state |H | <H c = 1.9 T (see Supplementary Fig. 10), and their signs depended on whether the control field H 0 and control current I 0 are parallel or antiparallel, confirming that the chirality control was successfully reproduced also for this sample.In Fig. 5g we plot the averaged NET of ΔR 2ω asym (|I 0 | ) = (R 2ω asym (+I 0 ) − R 2ω asym (−I 0 ))/2 as a function of |I 0 | .The magnitude of ΔR 2ω asym monotonically increases with increasing |I 0 | and tends to saturate.Figure 5c, d shows the H dependence of the transverse resistance R T after the chirality control procedure with the magnetic field H 0 and the electric current I 0 at 260 K.Note that the data for H > 0 T and H < 0 T were separately measured by sweeping the magnetic field from 0 T just after the chirality control procedure.The main contribution to R T seems to be from trivial effects such as longitudinal resistance, the Hall effect, and the planar Hall effect arising from the misalignments of voltage electrodes and the magnetic field.The slight difference between the positive and negative H 0 (Fig. 5c, d, respectively) for the same chirality should be ascribed to the magnetic hysteresis.Nevertheless, the apparent difference between the positive and negative I 0 for the same H 0 cannot be ascribed to any trivial effects.Because it is reversed by the reversal of H 0 , the nontrivial component seems to depend on whether H 0 and I 0 are parallel or antiparallel, as indicated by the dotted lines in Fig. 5c, d.At zero field, R T is around -1.48 mΩ for one chiral state (H 0 > 0, I 0 > 0 or H 0 < 0, I 0 < 0) and -1.57mΩ for the other (H 0 > 0, I 0 < 0 or H 0 < 0, I 0 > 0).Therefore, this quantity seems to be useful for probing the chirality at zero magnetic field.To examine the chirality dependence of R T , we calculate the difference between R T for positive and negative I 0 divided by 2, that is, ΔR T = (R T (+I 0 ) -R T (-I 0 ))/2 (Fig. 5e (H 0 > 0) and Fig. 5f (H 0 < 0)).ΔR T shows a maximum around 0 T and decreases with increasing H or decreasing H from H = 0 T.Then, it almost vanishes in the induced-ferromagnetic phase.The sign is reversed by the reversal of H 0 .These properties indicate that ΔR T reflects helimagnetic chirality.To confirm this, we have investigated the |I 0 | dependence of ΔR T (Fig. 5h).It is quite similar to the |I 0 | dependence of ΔR 2ω asym (Fig. 5g).In fact, ΔR T is proportional to ΔR 2ω asym , as shown in Fig. 5i.That is to say, ΔR T certainly reflects the helimagnetic chirality, which should be caused by the aforementioned spin accumulation mechanism.To further examine the mechanism, we also performed similar measurements on the MnAu 2 /Cu/Pt trilayer film sample and the MnAu 2 /W bilayer film sample (Supplementary Figs. 13,  14).In the case of the MnAu 2 /Cu/Pt trilayer film sample, ΔR T is rather enhanced, which indicates that the origin of ΔR T cannot be ascribed to some artifact originating from the MnAu 2 /Pt interface.For the MnAu 2 / W bilayer film sample, the sign of ΔR T is opposite to that of the MnAu 2 / Pt bilayer device, being consistent with the opposite signs of spin Hall conductance in Pt and W 32 .While we analyzed ΔR T in detail at 260 K since it was almost maximized, ΔR T is observed in a wide temperature range including room temperature (Supplementary Fig. 11).Therefore, ΔR T is useful as a chirality probe even at room temperature and does not require any magnetic field.

Discussion
In summary, we have demonstrated the chirality switching and detection in a room-temperature helimagnet MnAu 2 .The chirality degree of freedom is quite robust against magnetic disturbances and is free from the stray field problem.Similar electric current controls of the magnetic structure were performed for some antiferromagnets [36][37][38][39][40][41][42][43][44][45][46] .Some of them utilized symmetry breaking [36][37][38] and the others the spin current injection from the interface with spin Hall materials [39][40][41][42][43][44][45][46] .The threshold current density of j p = 1.4 × 10 10 A/m 2 for the chirality switching in the present work is relatively low compared to these works.Further reducing the electric current and extending the working temperature of chirality switching may be achieved by weakening the magnetic anisotropy by means of a suitable choice of substrate (see Supplementary Information, section 3).The transition temperature of T c = 335 K might be low for practical applications.In a bulk polycrystal, the helimagnetic transition temperature is as high as 360 K 17,18 .The lower transition temperature of 335 K in our thin film is possibly due to the epitaxial strain.The increase of the transition temperature up to 360 K or even higher should be feasible by improving the thin film growth condition.The transition temperature may be increased further by some chemical adjustments.For example, for another helimagnet CrAs, its transition temperature can be increased by 90 K (from 250 to 340 K) by the 14% substitution of As by Sb 47 .Therefore, the increase of transition temperature up to around 450 K may not be too ambitious.In addition, the thin film form of the sample enables us to utilize the interface-based functionality, the chirality-dependent transverse resistance.This result demonstrates current-induced spin accumulation originating from the Berry phase effect in the coplanar helimagnetic state, which is distinct from the well-known Berry phase effect of the emergent magnetic field in noncoplanar magnetic textures such as a skyrmion lattice [48][49][50] .A similar spin-polarization phenomenon known as chirality-induced spin selectivity (CISS) has been observed in chiral molecules and crystals 51,52 .The present observation can be viewed as a full magnetic analog of CISS.In a helimagnet with a nonchiral crystal structure, the magnetic CISS enables us to read out the chiral information even in the absence of magnetic fields.Because the transverse voltage is induced at the interface, the magnitude of transverse voltage is expected to become larger as the thickness of the thin film is reduced.If a highquality ultrathin film can be fabricated, the magnitude may satisfy the requirements for practical application as a probe of chirality-based magnetic memory.Thus, the present result is certainly a milestone for new technology helimagnetic spintronics.

Sample fabrication
Epitaxial films of MnAu 2 with a thickness of 100 nm were deposited on ScMgAlO 4 (10-10) substrates by magnetron sputtering from Mn and Au targets at 400 °C.To fabricate the sample for the measurements shown in Figs. 3, 4, one of the MnAu 2 films was in situ covered by a Ta cap layer with a thickness of 2 nm and annealed at 600 °C for 1 h.The thin Ta layer may be oxidized and less conductive, but we expected the MnAu 2 layer was almost free from oxidization, and the sample can be regarded as a single-layer MnAu 2 sample.To fabricate the MnAu 2 /Pt bilayer device, a Pt layer with the thickness of 10 nm was deposited on a MnAu 2 thin film at room temperature after annealed at 600 °C for 1 h.The XRD results indicate the epitaxial growth of MnAu 2 (110) on the ScMgAlO 4 (10-10) substrate, where the MnAu 2 [001] and the ScMgAlO 4 [0001] directions are parallel to each other (Supplementary Figs. 3 and 4).While a previous paper reports the growth of polycrystalline and multi-domain MnAu 2 films 53 , the suitable choice of substrate enabled the epitaxial growth of single crystalline films.The Pt layer in the bilayer device was revealed to be parallel to the (111) plane.The Pt layer is robust against oxidization and thicker than the Ta cap case.Therefore, the Pt/MnAu 2 sample can work as a bilayer device.

Magnetization measurement
The magnetization measurements were performed using a Magnetic Property Measurement System (Quantum Design).

First-and second-harmonic resistance measurement
For the resistance measurements, the thin film sample was patterned into Hall bar devices by photolithography and Ar plasma etching.Optical micrograph of the Hall bar device is shown in Fig. 2b.The direction of the electric current was parallel to the MnAu 2 [001] direction.The width of the Hall bars was 10 μm, and the distance between two voltage electrodes for the resistivity measurement was 25 μm.Electrical contacts were made by photolithography and electron beam evaporation of Ti (10 nm)/Au (100 nm).The longitudinal, transverse, and second-harmonic longitudinal ac resistances were measured by the lock-in technique with an ac electric current frequency of 11.15 Hz and an amplitude of 2 mA in a superconducting magnet or a Physical Property Measurement System (Quantum Design).For the MnAu 2 /Pt bilayer device shown in Fig. 5, we simultaneously measured the transverse resistance and second-harmonic longitudinal resistance.

Fig. 1 |
Fig.1| Concept of chirality control and chirality-dependent transverse resistance in helimagnets.a Schematic illustration of the effects of electron propagation along the propagation vector through a helimagnetic structure.The spin of conduction electron is rotated depending on the chirality, which induces the spin polarization along the wave vector.Reciprocally, the adiabatic spin-transfer torque (STT), non-adiabatic STT and the damping torque are exerted on the localized moments.The adiabatic STT rotates the magnetic structure within the helical plane, while the non-adiabatic STT and damping torques deform it conically.b Schematic illustration of the chirality control.The chirality corresponding to the handedness of the magnetic spiral is controlled by the electric current (j) and the magnetic field (H), depending on whether j and H are parallel or antiparallel.c Schematic illustration of the measurement setup for the transverse resistance in the helimagnet MnAu 2 /Pt bilayer device.The substrate is not shown for clarity.Electric current is applied parallel to the helimagnetic propagation vector (MnAu 2 [001] direction).The electric current in the helimagnetic MnAu 2 layer induces a chirality-dependent spin polarization.The accumulated spin polarization diffuses into the Pt layer, inducing the transverse voltage V T by means of the inverse spin Hall effect (ISHE).

Fig. 2 |
Fig. 2 | Properties of the MnAu 2 thin film.a Schematic illustration of the MnAu 2 thin film sample.MnAu 2 was epitaxially grown along the [110] direction with a thickness of 100 nm on a ScMgAlO 4 (10-10) substrate.The propagation vector of the helimagnetic structure is parallel to the [001] direction of MnAu 2 in the sample plane.The Ta cap layer (2 nm) is not shown for clarity.b Optical microscope image of the sample device.c Temperature T dependence of the magnetic susceptibility M/H, which is obtained by the magnetization M divided by the magnetic field H.The magnetic field as large as 0.1 T is applied along the [001] direction.d T dependence of the resistivity ρ.The electric current is applied along the [001] direction.e Magnetic phase diagram in the H-T plane for the MnAu 2 thin sample.The magnetic transition points are obtained by the magnetization and resistivity measurements.PM and induced FM denote the paramagnetic and field-induced ferromagnetic states, respectively.H c denotes the transition field from the helical phase to the induced-FM phase.The dashed line is merely a guide for the eyes.
Figure 5a, b shows the magnetic field H dependence of R 2ω

Fig. 5 |
Fig. 5 | Observation of the chirality-dependent transverse resistance in the MnAu 2 /Pt bilayer sample.a, b Magnetic field H dependence of R 2ω asym at 260 K after the field-sweep chirality control with the magnetic field H 0 = ±5 T and electric current I 0 = ±8.0mA for the MnAu 2 /Pt bilayer sample.The results for H 0 > 0 and H 0 < 0 are shown in (a, b), respectively.While the data of H < 0 are merely copies of the H > 0 data, we plot the H < 0 data just for clarity.The gray shading represents the induced-ferromagnetic (FM) phase.The ac electric current used for the R 2ω (H) measurement is 2.0 mA.c, d Magnetic field dependence of the transverse resistance R T after the chirality control with H 0 and I 0 for the MnAu 2 /Pt bilayer sample.The results for H 0 > 0 and H 0 < 0 are shown in (c, d), respectively.The horizontal dotted lines indicate the maxima of R T for the parallel and antiparallel H 0 and I 0 .e, f Magnetic field dependence of the chirality-dependent component of the transverse resistance estimated from the relation ΔR T = (R T (+I 0 ) -R T (-I 0 ))/2 for H 0 > 0 and H 0 < 0 are shown in (e, f), respectively.g |I 0 | dependence of −ΔR 2ω asym at 0.8 T for the MnAu 2 /Pt bilayer sample.Here, ΔR 2ω asym is the averaged NET signal (R 2ω asym (+I 0 ) -R 2ω asym (-I 0 ))/2.h |I 0 | dependence of ΔR T at 0 T for the MnAu 2 /Pt bilayer sample.i ΔR T at 0 T is plotted against −ΔR 2ω asym at 0.8 T. The gray line indicates the linear relation.